Quantum Oscillations in the Field-induced Ferromagnetic State of MnBi${}_{2-x}$Sb${}_x$Te${}_4$

The intrinsic antiferromagnetic topological insulator MnBi${}_2$Te${}_4$ undergoes a metamagnetic transition in a c-axis magnetic field. It has been predicted that ferromagnetic MnBi${}_2$Te${}_4$ is an ideal Weyl semimetal with a single pair of Weyl nodes. Here we report measurements of quantum oscillations detected in the field-induced ferromagnetic phase of MnBi${}_{2-x}$Sb${}_x$Te${}_4$, where Sb substitution tunes the majority carriers from electrons to holes. Single frequency Shubnikov-de Haas oscillations were observed in a wide range of Sb concentrations (0.54 $\le$ x $\le$ 1.21). The evolution of the oscillation frequency and the effective mass shows reasonable agreement with the Weyl semimetal band-structure of ferromagnetic MnBi${}_2$Te${}_4$ predicted by density functional calculations. Intriguingly, the quantum oscillation frequency shows a strong temperature dependence, indicating that the electronic structure sensitively depends on magnetism.